SAS Output

Chapter 4 Example: Means by StudyDay for Positive Mood outcome

The MEANS Procedure

Analysis Variable : posmood posmood: Positive Mood Rating (1 to 5)
N Obs	Mean	Std Error	Minimum	Maximum
1370	3.7173899	0.0200337	1.5238754	5.0000000

Analysis Variable : posmood posmood: Positive Mood Rating (1 to 5)
studyday: Day of Study (1 to 7)	N Obs	Mean	Std Error	Minimum	Maximum
1	192	3.6983522	0.0547996	1.8779325	5.0000000
2	195	3.7608782	0.0531300	1.6725632	5.0000000
3	194	3.6976149	0.0539275	1.6076257	5.0000000
4	197	3.7009648	0.0541752	1.6327778	5.0000000
5	197	3.7429638	0.0519959	1.6957540	5.0000000
6	196	3.7014449	0.0507846	1.5238754	5.0000000
7	199	3.7190701	0.0528145	1.7114225	5.0000000

Ch 4: Saturated Means, Unstructured R-Only Model

Test for mean differences across days

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structure	Unstructured
Subject Effect	PersonID
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	28
Columns in X	8
Columns in Z	0
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3094.36551632
1	2	2008.92067570	0.00333312
2	1	2008.02155902	0.00007663
3	1	2008.00217794	0.00000006
4	1	2008.00216370	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5955	0.4504	0.4098	0.4152	0.3970	0.3593	0.3518
2	0.4504	0.5640	0.3988	0.4285	0.4088	0.3549	0.3685
3	0.4098	0.3988	0.5772	0.4129	0.4145	0.3529	0.3888
4	0.4152	0.4285	0.4129	0.5884	0.4244	0.4138	0.3868
5	0.3970	0.4088	0.4145	0.4244	0.5417	0.3640	0.3822
6	0.3593	0.3549	0.3529	0.4138	0.3640	0.5120	0.3419
7	0.3518	0.3685	0.3888	0.3868	0.3822	0.3419	0.5570

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7772	0.6989	0.7015	0.6990	0.6506	0.6108
2	0.7772	1.0000	0.6990	0.7437	0.7396	0.6605	0.6574
3	0.6989	0.6990	1.0000	0.7085	0.7413	0.6491	0.6856
4	0.7015	0.7437	0.7085	1.0000	0.7517	0.7539	0.6757
5	0.6990	0.7396	0.7413	0.7517	1.0000	0.6911	0.6958
6	0.6506	0.6605	0.6491	0.7539	0.6911	1.0000	0.6403
7	0.6108	0.6574	0.6856	0.6757	0.6958	0.6403	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	0.5955	0.06116	9.74	<.0001
UN(2,1)	PersonID	0.4504	0.05286	8.52	<.0001
UN(2,2)	PersonID	0.5640	0.05741	9.83	<.0001
UN(3,1)	PersonID	0.4098	0.05163	7.94	<.0001
UN(3,2)	PersonID	0.3988	0.05000	7.98	<.0001
UN(3,3)	PersonID	0.5772	0.05887	9.81	<.0001
UN(4,1)	PersonID	0.4152	0.05184	8.01	<.0001
UN(4,2)	PersonID	0.4285	0.05138	8.34	<.0001
UN(4,3)	PersonID	0.4129	0.05108	8.08	<.0001
UN(4,4)	PersonID	0.5884	0.05952	9.89	<.0001
UN(5,1)	PersonID	0.3970	0.04965	8.00	<.0001
UN(5,2)	PersonID	0.4088	0.04919	8.31	<.0001
UN(5,3)	PersonID	0.4145	0.04982	8.32	<.0001
UN(5,4)	PersonID	0.4244	0.05040	8.42	<.0001
UN(5,5)	PersonID	0.5417	0.05482	9.88	<.0001
UN(6,1)	PersonID	0.3593	0.04718	7.61	<.0001
UN(6,2)	PersonID	0.3549	0.04602	7.71	<.0001
UN(6,3)	PersonID	0.3529	0.04643	7.60	<.0001
UN(6,4)	PersonID	0.4138	0.04911	8.43	<.0001
UN(6,5)	PersonID	0.3640	0.04569	7.97	<.0001
UN(6,6)	PersonID	0.5120	0.05190	9.86	<.0001
UN(7,1)	PersonID	0.3518	0.04837	7.27	<.0001
UN(7,2)	PersonID	0.3685	0.04781	7.71	<.0001
UN(7,3)	PersonID	0.3888	0.04910	7.92	<.0001
UN(7,4)	PersonID	0.3868	0.04927	7.85	<.0001
UN(7,5)	PersonID	0.3822	0.04764	8.02	<.0001
UN(7,6)	PersonID	0.3419	0.04526	7.56	<.0001
UN(7,7)	PersonID	0.5570	0.05602	9.94	<.0001

Fit Statistics
-2 Res Log Likelihood	2008.0
AIC (smaller is better)	2064.0
AICC (smaller is better)	2065.2
BIC (smaller is better)	2156.4

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
27	1086.36	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2008.0	28	2064.0	2065.2	2101.4	2156.4	2184.4

Solution for Fixed Effects
Effect	studyday: Day of Study (1 to 7)	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept		3.7233	0.05283	198	70.48	<.0001	0.05	3.6191	3.8275
studyday	1	0.01149	0.04790	199	0.24	0.8107	0.05	-0.08296	0.1059
studyday	2	0.05947	0.04415	200	1.35	0.1795	0.05	-0.02759	0.1465
studyday	3	-0.00083	0.04267	197	-0.02	0.9844	0.05	-0.08498	0.08331
studyday	4	-0.00677	0.04333	199	-0.16	0.8760	0.05	-0.09221	0.07867
studyday	5	0.03451	0.04111	199	0.84	0.4022	0.05	-0.04656	0.1156
studyday	6	-0.00575	0.04417	198	-0.13	0.8966	0.05	-0.09285	0.08135
studyday	7	0	.	.	.	.	.	.	.

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
studyday	6	197	4.65	0.78	0.5894	0.5904

Least Squares Means
Effect	studyday: Day of Study (1 to 7)	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
studyday	1	3.7348	0.05496	193	67.95	<.0001	0.05	3.6264	3.8432
studyday	2	3.7828	0.05332	195	70.94	<.0001	0.05	3.6776	3.8879
studyday	3	3.7225	0.05401	195	68.92	<.0001	0.05	3.6159	3.8290
studyday	4	3.7165	0.05436	197	68.37	<.0001	0.05	3.6093	3.8237
studyday	5	3.7578	0.05217	197	72.04	<.0001	0.05	3.6549	3.8607
studyday	6	3.7175	0.05079	196	73.20	<.0001	0.05	3.6174	3.8177
studyday	7	3.7233	0.05283	198	70.48	<.0001	0.05	3.6191	3.8275

Differences of Least Squares Means
Effect	studyday: Day of Study (1 to 7)	studyday: Day of Study (1 to 7)	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
studyday	1	2	-0.04798	0.03676	194	-1.31	0.1933	0.05	-0.1205	0.02452
studyday	1	3	0.01232	0.04286	196	0.29	0.7740	0.05	-0.07220	0.09684
studyday	1	4	0.01826	0.04269	197	0.43	0.6694	0.05	-0.06593	0.1024
studyday	1	5	-0.02302	0.04206	196	-0.55	0.5848	0.05	-0.1060	0.05994
studyday	1	6	0.01724	0.04481	197	0.38	0.7009	0.05	-0.07113	0.1056
studyday	1	7	0.01149	0.04790	199	0.24	0.8107	0.05	-0.08296	0.1059
studyday	2	3	0.06030	0.04208	197	1.43	0.1534	0.05	-0.02268	0.1433
studyday	2	4	0.06624	0.03888	196	1.70	0.0900	0.05	-0.01044	0.1429
studyday	2	5	0.02496	0.03839	197	0.65	0.5164	0.05	-0.05075	0.1007
studyday	2	6	0.06522	0.04328	196	1.51	0.1335	0.05	-0.02014	0.1506
studyday	2	7	0.05947	0.04415	200	1.35	0.1795	0.05	-0.02759	0.1465
studyday	3	4	0.005933	0.04172	195	0.14	0.8871	0.05	-0.07635	0.08821
studyday	3	5	-0.03535	0.03864	197	-0.91	0.3615	0.05	-0.1116	0.04086
studyday	3	6	0.004915	0.04436	195	0.11	0.9119	0.05	-0.08257	0.09240
studyday	3	7	-0.00083	0.04267	197	-0.02	0.9844	0.05	-0.08498	0.08331
studyday	4	5	-0.04128	0.03784	199	-1.09	0.2767	0.05	-0.1159	0.03335
studyday	4	6	-0.00102	0.03737	195	-0.03	0.9783	0.05	-0.07472	0.07269
studyday	4	7	-0.00677	0.04333	199	-0.16	0.8760	0.05	-0.09221	0.07867
studyday	5	6	0.04026	0.04074	197	0.99	0.3243	0.05	-0.04009	0.1206
studyday	5	7	0.03451	0.04111	199	0.84	0.4022	0.05	-0.04656	0.1156
studyday	6	7	-0.00575	0.04417	198	-0.13	0.8966	0.05	-0.09285	0.08135

Ch 4: Empty Means, Unstructured R-Only Model

Best-fitting and least parsimonious baseline

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structure	Unstructured
Subject Effect	PersonID
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	28
Columns in X	1
Columns in Z	0
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	1983.97011683	0.00294015
2	1	1983.12295859	0.00006042
3	1	1983.10659994	0.00000004
4	1	1983.10659001	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5954	0.4495	0.4107	0.4158	0.3970	0.3600	0.3526
2	0.4495	0.5632	0.3975	0.4265	0.4083	0.3534	0.3672
3	0.4107	0.3975	0.5775	0.4139	0.4141	0.3540	0.3896
4	0.4158	0.4265	0.4139	0.5885	0.4237	0.4146	0.3876
5	0.3970	0.4083	0.4141	0.4237	0.5407	0.3636	0.3818
6	0.3600	0.3534	0.3540	0.4146	0.3636	0.5121	0.3428
7	0.3526	0.3672	0.3896	0.3876	0.3818	0.3428	0.5565

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7763	0.7005	0.7025	0.6997	0.6521	0.6125
2	0.7763	1.0000	0.6970	0.7409	0.7399	0.6581	0.6558
3	0.7005	0.6970	1.0000	0.7100	0.7411	0.6510	0.6872
4	0.7025	0.7409	0.7100	1.0000	0.7511	0.7553	0.6774
5	0.6997	0.7399	0.7411	0.7511	1.0000	0.6910	0.6959
6	0.6521	0.6581	0.6510	0.7553	0.6910	1.0000	0.6420
7	0.6125	0.6558	0.6872	0.6774	0.6959	0.6420	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	0.5954	0.06103	9.75	<.0001
UN(2,1)	PersonID	0.4495	0.05278	8.52	<.0001
UN(2,2)	PersonID	0.5632	0.05739	9.81	<.0001
UN(3,1)	PersonID	0.4107	0.05160	7.96	<.0001
UN(3,2)	PersonID	0.3975	0.04992	7.96	<.0001
UN(3,3)	PersonID	0.5775	0.05881	9.82	<.0001
UN(4,1)	PersonID	0.4158	0.05180	8.03	<.0001
UN(4,2)	PersonID	0.4265	0.05124	8.32	<.0001
UN(4,3)	PersonID	0.4139	0.05109	8.10	<.0001
UN(4,4)	PersonID	0.5885	0.05947	9.90	<.0001
UN(5,1)	PersonID	0.3970	0.04957	8.01	<.0001
UN(5,2)	PersonID	0.4083	0.04918	8.30	<.0001
UN(5,3)	PersonID	0.4141	0.04974	8.33	<.0001
UN(5,4)	PersonID	0.4237	0.05029	8.42	<.0001
UN(5,5)	PersonID	0.5407	0.05467	9.89	<.0001
UN(6,1)	PersonID	0.3600	0.04717	7.63	<.0001
UN(6,2)	PersonID	0.3534	0.04594	7.69	<.0001
UN(6,3)	PersonID	0.3540	0.04646	7.62	<.0001
UN(6,4)	PersonID	0.4146	0.04913	8.44	<.0001
UN(6,5)	PersonID	0.3636	0.04562	7.97	<.0001
UN(6,6)	PersonID	0.5121	0.05188	9.87	<.0001
UN(7,1)	PersonID	0.3526	0.04832	7.30	<.0001
UN(7,2)	PersonID	0.3672	0.04771	7.70	<.0001
UN(7,3)	PersonID	0.3896	0.04909	7.94	<.0001
UN(7,4)	PersonID	0.3876	0.04926	7.87	<.0001
UN(7,5)	PersonID	0.3818	0.04755	8.03	<.0001
UN(7,6)	PersonID	0.3428	0.04527	7.57	<.0001
UN(7,7)	PersonID	0.5565	0.05591	9.95	<.0001

Fit Statistics
-2 Res Log Likelihood	1983.1
AIC (smaller is better)	2039.1
AICC (smaller is better)	2040.3
BIC (smaller is better)	2131.5

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
27	1090.35	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
1983.1	28	2039.1	2040.3	2076.5	2131.5	2159.5

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7353	0.04497	198	83.06	<.0001	0.05	3.6466	3.8240

Ch 4: Empty Means, Compound Symmetry R-Only Model

Worst-fitting and most parsimonious baseline

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structure	Compound Symmetry
Subject Effect	PersonID
Estimation Method	REML
Residual Variance Method	Profile
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	2
Columns in X	1
Columns in Z	0
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2029.21646328	0.00006140
2	1	2029.20127942	0.00000004
3	1	2029.20127059	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5604	0.3900	0.3900	0.3900	0.3900	0.3900	0.3900
2	0.3900	0.5604	0.3900	0.3900	0.3900	0.3900	0.3900
3	0.3900	0.3900	0.5604	0.3900	0.3900	0.3900	0.3900
4	0.3900	0.3900	0.3900	0.5604	0.3900	0.3900	0.3900
5	0.3900	0.3900	0.3900	0.3900	0.5604	0.3900	0.3900
6	0.3900	0.3900	0.3900	0.3900	0.3900	0.5604	0.3900
7	0.3900	0.3900	0.3900	0.3900	0.3900	0.3900	0.5604

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.6959	0.6959	0.6959	0.6959	0.6959	0.6959
2	0.6959	1.0000	0.6959	0.6959	0.6959	0.6959	0.6959
3	0.6959	0.6959	1.0000	0.6959	0.6959	0.6959	0.6959
4	0.6959	0.6959	0.6959	1.0000	0.6959	0.6959	0.6959
5	0.6959	0.6959	0.6959	0.6959	1.0000	0.6959	0.6959
6	0.6959	0.6959	0.6959	0.6959	0.6959	1.0000	0.6959
7	0.6959	0.6959	0.6959	0.6959	0.6959	0.6959	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
CS	PersonID	0.3900	0.04171	9.35	<.0001
Residual		0.1704	0.007049	24.18	<.0001

Fit Statistics
-2 Res Log Likelihood	2029.2
AIC (smaller is better)	2033.2
AICC (smaller is better)	2033.2
BIC (smaller is better)	2039.8

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
1	1044.25	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2029.2	2	2033.2	2033.2	2035.9	2039.8	2041.8

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7356	0.04556	198	82.00	<.0001	0.05	3.6458	3.8255

Likelihood Ratio Test for CS vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
CS	2029.2	2	2033.2	2039.8	.	.	.
UN	1983.1	28	2039.1	2131.5	46.0947	26	.008902137

Ch 4: Empty Means, Compound Symmetry Heterogeneous R-Only Model

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structure	Heterogeneous Compound Symmetry
Subject Effect	PersonID
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	8
Columns in X	1
Columns in Z	0
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2026.16573253	0.00026419
2	1	2026.09973370	0.00000031
3	1	2026.09965872	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5974	0.3994	0.4088	0.4058	0.3895	0.3906	0.4112
2	0.3994	0.5504	0.3924	0.3895	0.3739	0.3749	0.3947
3	0.4088	0.3924	0.5766	0.3987	0.3827	0.3837	0.4040
4	0.4058	0.3895	0.3987	0.5682	0.3799	0.3809	0.4010
5	0.3895	0.3739	0.3827	0.3799	0.5234	0.3656	0.3849
6	0.3906	0.3749	0.3837	0.3809	0.3656	0.5263	0.3860
7	0.4112	0.3947	0.4040	0.4010	0.3849	0.3860	0.5835

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.6965	0.6965	0.6965	0.6965	0.6965	0.6965
2	0.6965	1.0000	0.6965	0.6965	0.6965	0.6965	0.6965
3	0.6965	0.6965	1.0000	0.6965	0.6965	0.6965	0.6965
4	0.6965	0.6965	0.6965	1.0000	0.6965	0.6965	0.6965
5	0.6965	0.6965	0.6965	0.6965	1.0000	0.6965	0.6965
6	0.6965	0.6965	0.6965	0.6965	0.6965	1.0000	0.6965
7	0.6965	0.6965	0.6965	0.6965	0.6965	0.6965	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
Var(1)	PersonID	0.5974	0.06015	9.93	<.0001
Var(2)	PersonID	0.5504	0.05482	10.04	<.0001
Var(3)	PersonID	0.5766	0.05771	9.99	<.0001
Var(4)	PersonID	0.5682	0.05611	10.13	<.0001
Var(5)	PersonID	0.5234	0.05170	10.12	<.0001
Var(6)	PersonID	0.5263	0.05278	9.97	<.0001
Var(7)	PersonID	0.5835	0.05837	10.00	<.0001
CSH	PersonID	0.6965	0.02445	28.49	<.0001

Fit Statistics
-2 Res Log Likelihood	2026.1
AIC (smaller is better)	2042.1
AICC (smaller is better)	2042.2
BIC (smaller is better)	2068.5

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
7	1047.36	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2026.1	8	2042.1	2042.2	2052.8	2068.5	2076.5

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7387	0.04533	200	82.47	<.0001	0.05	3.6493	3.8281

Likelihood Ratio Test for CSH vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
CSH	2026.1	8	2042.1	2068.5	.	.	.
UN	1983.1	28	2039.1	2131.5	42.9931	20	.002048638

Likelihood Ratio Test for CS vs. CSH

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
CS	2029.2	2	2033.2	2039.8	.	.	.
CSH	2026.1	8	2042.1	2068.5	3.10161	6	0.79599

Ch 4: Empty Means, First-Order Auto-Regressive R-Only Model

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structure	Autoregressive
Subject Effect	PersonID
Estimation Method	REML
Residual Variance Method	Profile
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	2
Columns in X	1
Columns in Z	0
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2279.79681869	0.00003970
2	1	2279.79212251	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5627	0.4012	0.2860	0.2039	0.1454	0.1037	0.07390
2	0.4012	0.5627	0.4012	0.2860	0.2039	0.1454	0.1037
3	0.2860	0.4012	0.5627	0.4012	0.2860	0.2039	0.1454
4	0.2039	0.2860	0.4012	0.5627	0.4012	0.2860	0.2039
5	0.1454	0.2039	0.2860	0.4012	0.5627	0.4012	0.2860
6	0.1037	0.1454	0.2039	0.2860	0.4012	0.5627	0.4012
7	0.07390	0.1037	0.1454	0.2039	0.2860	0.4012	0.5627

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7130	0.5083	0.3624	0.2584	0.1842	0.1313
2	0.7130	1.0000	0.7130	0.5083	0.3624	0.2584	0.1842
3	0.5083	0.7130	1.0000	0.7130	0.5083	0.3624	0.2584
4	0.3624	0.5083	0.7130	1.0000	0.7130	0.5083	0.3624
5	0.2584	0.3624	0.5083	0.7130	1.0000	0.7130	0.5083
6	0.1842	0.2584	0.3624	0.5083	0.7130	1.0000	0.7130
7	0.1313	0.1842	0.2584	0.3624	0.5083	0.7130	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
AR(1)	PersonID	0.7130	0.01816	39.25	<.0001
Residual		0.5627	0.03315	16.98	<.0001

Fit Statistics
-2 Res Log Likelihood	2279.8
AIC (smaller is better)	2283.8
AICC (smaller is better)	2283.8
BIC (smaller is better)	2290.4

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
1	793.66	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2279.8	2	2283.8	2283.8	2286.5	2290.4	2292.4

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7312	0.03756	246	99.35	<.0001	0.05	3.6572	3.8052

Likelihood Ratio Test for AR1 vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
AR1	2279.8	2	2283.8	2290.4	.	.	.
UN	1983.1	28	2039.1	2131.5	296.686	26	0

Ch 4: Empty Means, First-Order Auto-Regressive Heterogeneous R-Only Model

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structure	Heterogeneous Autoregressive
Subject Effect	PersonID
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	8
Columns in X	1
Columns in Z	0
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2277.85816026	0.00123729
2	1	2277.70855760	0.00000070
3	1	2277.70847411	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5440	0.3825	0.2827	0.2002	0.1389	0.1005	0.07472
2	0.3825	0.5312	0.3926	0.2780	0.1928	0.1395	0.1038
3	0.2827	0.3926	0.5731	0.4059	0.2815	0.2037	0.1515
4	0.2002	0.2780	0.4059	0.5676	0.3937	0.2848	0.2118
5	0.1389	0.1928	0.2815	0.3937	0.5393	0.3902	0.2902
6	0.1005	0.1395	0.2037	0.2848	0.3902	0.5576	0.4147
7	0.07472	0.1038	0.1515	0.2118	0.2902	0.4147	0.6092

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7115	0.5063	0.3603	0.2563	0.1824	0.1298
2	0.7115	1.0000	0.7115	0.5063	0.3603	0.2563	0.1824
3	0.5063	0.7115	1.0000	0.7115	0.5063	0.3603	0.2563
4	0.3603	0.5063	0.7115	1.0000	0.7115	0.5063	0.3603
5	0.2563	0.3603	0.5063	0.7115	1.0000	0.7115	0.5063
6	0.1824	0.2563	0.3603	0.5063	0.7115	1.0000	0.7115
7	0.1298	0.1824	0.2563	0.3603	0.5063	0.7115	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
Var(1)	PersonID	0.5440	0.04994	10.89	<.0001
Var(2)	PersonID	0.5312	0.04780	11.11	<.0001
Var(3)	PersonID	0.5731	0.05311	10.79	<.0001
Var(4)	PersonID	0.5676	0.05242	10.83	<.0001
Var(5)	PersonID	0.5393	0.05017	10.75	<.0001
Var(6)	PersonID	0.5576	0.05235	10.65	<.0001
Var(7)	PersonID	0.6092	0.05783	10.53	<.0001
ARH(1)	PersonID	0.7115	0.01867	38.10	<.0001

Fit Statistics
-2 Res Log Likelihood	2277.7
AIC (smaller is better)	2293.7
AICC (smaller is better)	2293.8
BIC (smaller is better)	2320.1

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
7	795.75	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2277.7	8	2293.7	2293.8	2304.4	2320.1	2328.1

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7348	0.03754	247	99.49	<.0001	0.05	3.6609	3.8088

Likelihood Ratio Test for ARH1 vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
ARH1	2277.7	8	2293.7	2320.1	.	.	.
UN	1983.1	28	2039.1	2131.5	294.602	20	0

Likelihood Ratio Test for AR1 vs. ARH1

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
AR1	2279.8	2	2283.8	2290.4	.	.	.
ARH1	2277.7	8	2293.7	2320.1	2.08365	6	0.91185

Ch 4: Empty Means, n-1 Lag Toeplitz R-Only Model

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structure	Toeplitz
Subject Effect	PersonID
Estimation Method	REML
Residual Variance Method	Profile
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	7
Columns in X	1
Columns in Z	0
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2009.94324985	0.00014451
2	1	2009.90612566	0.00000008
3	1	2009.90610463	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5609	0.3986	0.4063	0.3851	0.3823	0.3709	0.3477
2	0.3986	0.5609	0.3986	0.4063	0.3851	0.3823	0.3709
3	0.4063	0.3986	0.5609	0.3986	0.4063	0.3851	0.3823
4	0.3851	0.4063	0.3986	0.5609	0.3986	0.4063	0.3851
5	0.3823	0.3851	0.4063	0.3986	0.5609	0.3986	0.4063
6	0.3709	0.3823	0.3851	0.4063	0.3986	0.5609	0.3986
7	0.3477	0.3709	0.3823	0.3851	0.4063	0.3986	0.5609

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7106	0.7243	0.6865	0.6816	0.6613	0.6199
2	0.7106	1.0000	0.7106	0.7243	0.6865	0.6816	0.6613
3	0.7243	0.7106	1.0000	0.7106	0.7243	0.6865	0.6816
4	0.6865	0.7243	0.7106	1.0000	0.7106	0.7243	0.6865
5	0.6816	0.6865	0.7243	0.7106	1.0000	0.7106	0.7243
6	0.6613	0.6816	0.6865	0.7243	0.7106	1.0000	0.7106
7	0.6199	0.6613	0.6816	0.6865	0.7243	0.7106	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
TOEP(2)	PersonID	0.3986	0.04200	9.49	<.0001
TOEP(3)	PersonID	0.4063	0.04197	9.68	<.0001
TOEP(4)	PersonID	0.3851	0.04195	9.18	<.0001
TOEP(5)	PersonID	0.3823	0.04219	9.06	<.0001
TOEP(6)	PersonID	0.3709	0.04269	8.69	<.0001
TOEP(7)	PersonID	0.3477	0.04398	7.91	<.0001
Residual		0.5609	0.04210	13.32	<.0001

Fit Statistics
-2 Res Log Likelihood	2009.9
AIC (smaller is better)	2023.9
AICC (smaller is better)	2024.0
BIC (smaller is better)	2047.0

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
6	1063.55	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2009.9	7	2023.9	2024.0	2033.2	2047.0	2054.0

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7357	0.04552	198	82.07	<.0001	0.05	3.6460	3.8255

Likelihood Ratio Test for TOEP7 vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
TOEP7	2009.9	7	2023.9	2047.0	.	.	.
UN	1983.1	28	2039.1	2131.5	26.7995	21	0.17759

Likelihood Ratio Test for CS vs. TOEP7

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
CS	2029.2	2	2033.2	2039.8	.	.	.
TOEP7	2009.9	7	2023.9	2047.0	19.2952	5	.001693337

Likelihood Ratio Test for AR1 vs. TOEP7

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
AR1	2279.8	2	2283.8	2290.4	.	.	.
TOEP7	2009.9	7	2023.9	2047.0	269.886	5	0

Ch 4: Empty Means, n-1 Lag Toeplitz Heterogeneous R-Only Model

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structure	Heterogeneous Toeplitz
Subject Effect	PersonID
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	13
Columns in X	1
Columns in Z	0
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2007.75048447	0.00071851
2	1	2007.55993815	0.00000361
3	1	2007.55901592	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5803	0.3987	0.4211	0.3960	0.3798	0.3650	0.3591
2	0.3987	0.5441	0.3993	0.4047	0.3708	0.3641	0.3709
3	0.4211	0.3993	0.5820	0.4099	0.4047	0.3796	0.3952
4	0.3960	0.4047	0.4099	0.5734	0.3934	0.3977	0.3954
5	0.3798	0.3708	0.4047	0.3934	0.5361	0.3766	0.4036
6	0.3650	0.3641	0.3796	0.3977	0.3766	0.5254	0.3912
7	0.3591	0.3709	0.3952	0.3954	0.4036	0.3912	0.5786

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7096	0.7246	0.6865	0.6809	0.6611	0.6197
2	0.7096	1.0000	0.7096	0.7246	0.6865	0.6809	0.6611
3	0.7246	0.7096	1.0000	0.7096	0.7246	0.6865	0.6809
4	0.6865	0.7246	0.7096	1.0000	0.7096	0.7246	0.6865
5	0.6809	0.6865	0.7246	0.7096	1.0000	0.7096	0.7246
6	0.6611	0.6809	0.6865	0.7246	0.7096	1.0000	0.7096
7	0.6197	0.6611	0.6809	0.6865	0.7246	0.7096	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
Var(1)	PersonID	0.5803	0.05778	10.04	<.0001
Var(2)	PersonID	0.5441	0.05394	10.09	<.0001
Var(3)	PersonID	0.5820	0.05825	9.99	<.0001
Var(4)	PersonID	0.5734	0.05672	10.11	<.0001
Var(5)	PersonID	0.5361	0.05326	10.07	<.0001
Var(6)	PersonID	0.5254	0.05265	9.98	<.0001
Var(7)	PersonID	0.5786	0.05750	10.06	<.0001
TOEPH(1)	PersonID	0.7096	0.02482	28.58	<.0001
TOEPH(2)	PersonID	0.7246	0.02355	30.76	<.0001
TOEPH(3)	PersonID	0.6865	0.02704	25.39	<.0001
TOEPH(4)	PersonID	0.6809	0.02866	23.76	<.0001
TOEPH(5)	PersonID	0.6611	0.03245	20.38	<.0001
TOEPH(6)	PersonID	0.6197	0.04130	15.00	<.0001

Fit Statistics
-2 Res Log Likelihood	2007.6
AIC (smaller is better)	2033.6
AICC (smaller is better)	2033.8
BIC (smaller is better)	2076.4

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
12	1065.90	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2007.6	13	2033.6	2033.8	2050.9	2076.4	2089.4

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7400	0.04533	199	82.50	<.0001	0.05	3.6506	3.8294

Likelihood Ratio Test for TOEPH7 vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
TOEPH7	2007.6	13	2033.6	2076.4	.	.	.
UN	1983.1	28	2039.1	2131.5	24.4524	15	0.057798

Likelihood Ratio Test for TOEP7 vs. TOEPH7

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
TOEP7	2009.9	7	2023.9	2047.0	.	.	.
TOEPH7	2007.6	13	2033.6	2076.4	2.34709	6	0.88517

Likelihood Ratio Test for CSH vs. TOEPH7

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
CSH	2026.1	8	2042.1	2068.5	.	.	.
TOEPH7	2007.6	13	2033.6	2076.4	18.5406	5	.002339852

Likelihood Ratio Test for ARH1 vs. TOEPH7

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
ARH1	2277.7	8	2293.7	2320.1	.	.	.
TOEPH7	2007.6	13	2033.6	2076.4	270.149	5	0

Ch 4: Empty Means, Random Intercept in G

n-1 Order Unstructured R

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structure	Unstructured
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	29
Columns in X	1
Columns in Z Per Subject	1
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	1983.97011683	0.00294015
2	1	1983.12295859	0.00006042
3	1	1983.10659994	0.00000004
4	1	1983.10659001	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.2428	0.09693	0.05816	0.06325	0.04441	0.007464
2	0.09693	0.2106	0.04490	0.07393	0.05569	0.000857	0.01457
3	0.05816	0.04490	0.2249	0.06133	0.06151	0.001445	0.03697
4	0.06325	0.07393	0.06133	0.2359	0.07108	0.06206	0.03506
5	0.04441	0.05569	0.06151	0.07108	0.1881	0.01104	0.02918
6	0.007464	0.000857	0.001445	0.06206	0.01104	0.1595	-0.00982
7		0.01457	0.03697	0.03506	0.02918	-0.00982	0.2039

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.4287	0.2489	0.2643	0.2078	0.03793
2	0.4287	1.0000	0.2063	0.3317	0.2798	0.004677	0.07033
3	0.2489	0.2063	1.0000	0.2663	0.2991	0.007628	0.1726
4	0.2643	0.3317	0.2663	1.0000	0.3374	0.3199	0.1598
5	0.2078	0.2798	0.2991	0.3374	1.0000	0.06373	0.1490
6	0.03793	0.004677	0.007628	0.3199	0.06373	1.0000	-0.05442
7		0.07033	0.1726	0.1598	0.1490	-0.05442	1.0000

Estimated G Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	0.3526

Estimated G Correlation Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	1.0000

Estimated V Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5954	0.4495	0.4107	0.4158	0.3970	0.3600	0.3526
2	0.4495	0.5632	0.3975	0.4265	0.4083	0.3534	0.3672
3	0.4107	0.3975	0.5775	0.4139	0.4141	0.3540	0.3896
4	0.4158	0.4265	0.4139	0.5885	0.4237	0.4146	0.3876
5	0.3970	0.4083	0.4141	0.4237	0.5407	0.3636	0.3818
6	0.3600	0.3534	0.3540	0.4146	0.3636	0.5121	0.3428
7	0.3526	0.3672	0.3896	0.3876	0.3818	0.3428	0.5565

Estimated V Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7763	0.7005	0.7025	0.6997	0.6521	0.6125
2	0.7763	1.0000	0.6970	0.7409	0.7399	0.6581	0.6558
3	0.7005	0.6970	1.0000	0.7100	0.7411	0.6510	0.6872
4	0.7025	0.7409	0.7100	1.0000	0.7511	0.7553	0.6774
5	0.6997	0.7399	0.7411	0.7511	1.0000	0.6910	0.6959
6	0.6521	0.6581	0.6510	0.7553	0.6910	1.0000	0.6420
7	0.6125	0.6558	0.6872	0.6774	0.6959	0.6420	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	0.3526	0.04832	7.30	<.0001
UN(1,1)	PersonID	0.2428	0.04127	5.88	<.0001
UN(2,1)	PersonID	0.09693	0.03535	2.74	0.0061
UN(2,2)	PersonID	0.2106	0.04800	4.39	<.0001
UN(3,1)	PersonID	0.05816	0.03362	1.73	0.0837
UN(3,2)	PersonID	0.04490	0.03923	1.14	0.2524
UN(3,3)	PersonID	0.2249	0.05067	4.44	<.0001
UN(4,1)	PersonID	0.06325	0.03392	1.86	0.0622
UN(4,2)	PersonID	0.07393	0.04083	1.81	0.0702
UN(4,3)	PersonID	0.06133	0.04134	1.48	0.1379
UN(4,4)	PersonID	0.2359	0.05126	4.60	<.0001
UN(5,1)	PersonID	0.04441	0.03213	1.38	0.1669
UN(5,2)	PersonID	0.05569	0.03948	1.41	0.1583
UN(5,3)	PersonID	0.06151	0.04090	1.50	0.1326
UN(5,4)	PersonID	0.07108	0.04145	1.71	0.0864
UN(5,5)	PersonID	0.1881	0.04770	3.94	<.0001
UN(6,1)	PersonID	0.007464	0.03435	0.22	0.8280
UN(6,2)	PersonID	0.000857	0.03954	0.02	0.9827
UN(6,3)	PersonID	0.001445	0.04077	0.04	0.9717
UN(6,4)	PersonID	0.06206	0.04369	1.42	0.1555
UN(6,5)	PersonID	0.01104	0.04078	0.27	0.7866
UN(6,6)	PersonID	0.1595	0.05039	3.17	0.0008
UN(7,1)	PersonID	0	.	.	.
UN(7,2)	PersonID	0.01457	0.02792	0.52	0.6017
UN(7,3)	PersonID	0.03697	0.03250	1.14	0.2554
UN(7,4)	PersonID	0.03506	0.03228	1.09	0.2774
UN(7,5)	PersonID	0.02918	0.03170	0.92	0.3573
UN(7,6)	PersonID	-0.00982	0.03368	-0.29	0.7707
UN(7,7)	PersonID	0.2039	0.03864	5.28	<.0001

Fit Statistics
-2 Res Log Likelihood	1983.1
AIC (smaller is better)	2039.1
AICC (smaller is better)	2040.3
BIC (smaller is better)	2131.5

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
27	1090.35	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
1983.1	28	2039.1	2040.3	2076.5	2131.5	2159.5

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7353	0.04497	198	83.06	<.0001	0.05	3.6466	3.8240

Ch 4: Empty Means, Random Intercept in G

Diagonal R

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structures	Unstructured, Variance Components
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	2
Columns in X	1
Columns in Z Per Subject	1
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2029.22241046	0.00008619
2	1	2029.20127335	0.00000001
3	1	2029.20127059	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.1704
2		0.1704
3			0.1704
4				0.1704
5					0.1704
6						0.1704
7							0.1704

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000
2		1.0000
3			1.0000
4				1.0000
5					1.0000
6						1.0000
7							1.0000

Estimated G Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	0.3900

Estimated G Correlation Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	1.0000

Estimated V Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5604	0.3900	0.3900	0.3900	0.3900	0.3900	0.3900
2	0.3900	0.5604	0.3900	0.3900	0.3900	0.3900	0.3900
3	0.3900	0.3900	0.5604	0.3900	0.3900	0.3900	0.3900
4	0.3900	0.3900	0.3900	0.5604	0.3900	0.3900	0.3900
5	0.3900	0.3900	0.3900	0.3900	0.5604	0.3900	0.3900
6	0.3900	0.3900	0.3900	0.3900	0.3900	0.5604	0.3900
7	0.3900	0.3900	0.3900	0.3900	0.3900	0.3900	0.5604

Estimated V Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.6959	0.6959	0.6959	0.6959	0.6959	0.6959
2	0.6959	1.0000	0.6959	0.6959	0.6959	0.6959	0.6959
3	0.6959	0.6959	1.0000	0.6959	0.6959	0.6959	0.6959
4	0.6959	0.6959	0.6959	1.0000	0.6959	0.6959	0.6959
5	0.6959	0.6959	0.6959	0.6959	1.0000	0.6959	0.6959
6	0.6959	0.6959	0.6959	0.6959	0.6959	1.0000	0.6959
7	0.6959	0.6959	0.6959	0.6959	0.6959	0.6959	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr > Z
UN(1,1)	PersonID	0.3900	0.04171	9.35	<.0001
studyday	PersonID	0.1704	0.007049	24.18	<.0001

Fit Statistics
-2 Res Log Likelihood	2029.2
AIC (smaller is better)	2033.2
AICC (smaller is better)	2033.2
BIC (smaller is better)	2039.8

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
1	1044.25	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2029.2	2	2033.2	2033.2	2035.9	2039.8	2041.8

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7356	0.04556	198	82.00	<.0001	0.05	3.6458	3.8255

Likelihood Ratio Test for RIDIAG vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RIDIAG	2029.2	2	2033.2	2039.8	.	.	.
UN	1983.1	28	2039.1	2131.5	46.0947	26	.008902137

Ch 4: Empty Means, Random Intercept in G

Diagonal Heterogeneous R

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structure	Unstructured
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	29
Columns in X	1
Columns in Z Per Subject	1
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2029.82614852	0.03374688
2	1	2020.07719755	0.00481375
3	1	2018.75249350	0.00017705
4	1	2018.70729428	0.00000030
5	1	2018.70721869	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.1886
2		0.1529
3			0.1762
4				0.1478
5					0.1354
6						0.1786
7							0.2116

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000
2		1.0000
3			1.0000
4				1.0000
5					1.0000
6						1.0000
7							1.0000

Estimated G Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	0.3936

Estimated G Correlation Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	1.0000

Estimated V Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5823	0.3936	0.3936	0.3936	0.3936	0.3936	0.3936
2	0.3936	0.5466	0.3936	0.3936	0.3936	0.3936	0.3936
3	0.3936	0.3936	0.5698	0.3936	0.3936	0.3936	0.3936
4	0.3936	0.3936	0.3936	0.5414	0.3936	0.3936	0.3936
5	0.3936	0.3936	0.3936	0.3936	0.5290	0.3936	0.3936
6	0.3936	0.3936	0.3936	0.3936	0.3936	0.5722	0.3936
7	0.3936	0.3936	0.3936	0.3936	0.3936	0.3936	0.6052

Estimated V Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.6978	0.6834	0.7011	0.7092	0.6819	0.6631
2	0.6978	1.0000	0.7054	0.7236	0.7320	0.7039	0.6844
3	0.6834	0.7054	1.0000	0.7087	0.7170	0.6894	0.6703
4	0.7011	0.7236	0.7087	1.0000	0.7355	0.7072	0.6877
5	0.7092	0.7320	0.7170	0.7355	1.0000	0.7154	0.6957
6	0.6819	0.7039	0.6894	0.7072	0.7154	1.0000	0.6689
7	0.6631	0.6844	0.6703	0.6877	0.6957	0.6689	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr > Z
UN(1,1)	PersonID	0.3936	0.04206	9.36	<.0001
UN(1,1)	PersonID	0.1886	0.02201	8.57	<.0001
UN(2,1)	PersonID	0	.	.	.
UN(2,2)	PersonID	0.1529	0.01833	8.34	<.0001
UN(3,1)	PersonID	0	.	.	.
UN(3,2)	PersonID	0	.	.	.
UN(3,3)	PersonID	0.1762	0.02060	8.55	<.0001
UN(4,1)	PersonID	0	.	.	.
UN(4,2)	PersonID	0	.	.	.
UN(4,3)	PersonID	0	.	.	.
UN(4,4)	PersonID	0.1478	0.01769	8.35	<.0001
UN(5,1)	PersonID	0	.	.	.
UN(5,2)	PersonID	0	.	.	.
UN(5,3)	PersonID	0	.	.	.
UN(5,4)	PersonID	0	.	.	.
UN(5,5)	PersonID	0.1354	0.01645	8.23	<.0001
UN(6,1)	PersonID	0	.	.	.
UN(6,2)	PersonID	0	.	.	.
UN(6,3)	PersonID	0	.	.	.
UN(6,4)	PersonID	0	.	.	.
UN(6,5)	PersonID	0	.	.	.
UN(6,6)	PersonID	0.1786	0.02083	8.58	<.0001
UN(7,1)	PersonID	0	.	.	.
UN(7,2)	PersonID	0	.	.	.
UN(7,3)	PersonID	0	.	.	.
UN(7,4)	PersonID	0	.	.	.
UN(7,5)	PersonID	0	.	.	.
UN(7,6)	PersonID	0	.	.	.
UN(7,7)	PersonID	0.2116	0.02382	8.88	<.0001

Fit Statistics
-2 Res Log Likelihood	2018.7
AIC (smaller is better)	2034.7
AICC (smaller is better)	2034.8
BIC (smaller is better)	2061.1

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
7	1054.75	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2018.7	8	2034.7	2034.8	2045.4	2061.1	2069.1

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7373	0.04573	198	81.73	<.0001	0.05	3.6471	3.8275

Likelihood Ratio Test for RIDIAGH vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RIDIAGH	2018.7	8	2034.7	2061.1	.	.	.
UN	1983.1	28	2039.1	2131.5	35.6006	20	0.017129

Likelihood Ratio Test for RIDIAG vs. RIDIAGH

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RIDIAG	2029.2	2	2033.2	2039.8	.	.	.
RIDIAGH	2018.7	8	2034.7	2061.1	10.4941	6	0.10533

Ch 4: Empty Means, Random Intercept in G

First-Order Autoregressive R

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structures	Unstructured, Autoregressive
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Profile
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	3
Columns in X	1
Columns in Z Per Subject	1
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2027.43636266	0.00005959
2	1	2027.42157436	0.00000003
3	1	2027.42156589	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.1730	0.008484	0.000416	0.000020	1.001E-6	4.911E-8	2.409E-9
2	0.008484	0.1730	0.008484	0.000416	0.000020	1.001E-6	4.911E-8
3	0.000416	0.008484	0.1730	0.008484	0.000416	0.000020	1.001E-6
4	0.000020	0.000416	0.008484	0.1730	0.008484	0.000416	0.000020
5	1.001E-6	0.000020	0.000416	0.008484	0.1730	0.008484	0.000416
6	4.911E-8	1.001E-6	0.000020	0.000416	0.008484	0.1730	0.008484
7	2.409E-9	4.911E-8	1.001E-6	0.000020	0.000416	0.008484	0.1730

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.04905	0.002406	0.000118	5.789E-6	2.839E-7	1.393E-8
2	0.04905	1.0000	0.04905	0.002406	0.000118	5.789E-6	2.839E-7
3	0.002406	0.04905	1.0000	0.04905	0.002406	0.000118	5.789E-6
4	0.000118	0.002406	0.04905	1.0000	0.04905	0.002406	0.000118
5	5.789E-6	0.000118	0.002406	0.04905	1.0000	0.04905	0.002406
6	2.839E-7	5.789E-6	0.000118	0.002406	0.04905	1.0000	0.04905
7	1.393E-8	2.839E-7	5.789E-6	0.000118	0.002406	0.04905	1.0000

Estimated G Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	0.3875

Estimated G Correlation Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	1.0000

Estimated V Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5605	0.3960	0.3879	0.3875	0.3875	0.3875	0.3875
2	0.3960	0.5605	0.3960	0.3879	0.3875	0.3875	0.3875
3	0.3879	0.3960	0.5605	0.3960	0.3879	0.3875	0.3875
4	0.3875	0.3879	0.3960	0.5605	0.3960	0.3879	0.3875
5	0.3875	0.3875	0.3879	0.3960	0.5605	0.3960	0.3879
6	0.3875	0.3875	0.3875	0.3879	0.3960	0.5605	0.3960
7	0.3875	0.3875	0.3875	0.3875	0.3879	0.3960	0.5605

Estimated V Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7065	0.6921	0.6914	0.6914	0.6914	0.6914
2	0.7065	1.0000	0.7065	0.6921	0.6914	0.6914	0.6914
3	0.6921	0.7065	1.0000	0.7065	0.6921	0.6914	0.6914
4	0.6914	0.6921	0.7065	1.0000	0.7065	0.6921	0.6914
5	0.6914	0.6914	0.6921	0.7065	1.0000	0.7065	0.6921
6	0.6914	0.6914	0.6914	0.6921	0.7065	1.0000	0.7065
7	0.6914	0.6914	0.6914	0.6914	0.6921	0.7065	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	0.3875	0.04177	9.28	<.0001
AR(1)	PersonID	0.04905	0.03708	1.32	0.1859
Residual		0.1730	0.007558	22.89	<.0001

Fit Statistics
-2 Res Log Likelihood	2027.4
AIC (smaller is better)	2033.4
AICC (smaller is better)	2033.4
BIC (smaller is better)	2043.3

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
2	1046.03	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2027.4	3	2033.4	2033.4	2037.4	2043.3	2046.3

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7356	0.04556	198	82.00	<.0001	0.05	3.6457	3.8254

Likelihood Ratio Test for RIAR1 vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RIAR1	2027.4	3	2033.4	2043.3	.	.	.
UN	1983.1	28	2039.1	2131.5	44.3150	25	.009997744

Likelihood Ratio Test for AR1 vs. RIAR1

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
AR1	2279.8	2	2283.8	2290.4	.	.	.
RIAR1	2027.4	3	2033.4	2043.3	252.371	1	0

Likelihood Ratio Test for RIDIAG vs. RIAR1

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RIDIAG	2029.2	2	2033.2	2039.8	.	.	.
RIAR1	2027.4	3	2033.4	2043.3	1.77970	1	0.18219

Ch 4: Empty Means, Random Intercept in G

First-Order Autoregressive Heterogeneous R

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structures	Unstructured, Heterogeneous Autoregressive
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	9
Columns in X	1
Columns in Z Per Subject	1
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2029.30979779	0.03437887
2	1	2019.35946081	0.00508064
3	1	2017.95308844	0.00020570
4	1	2017.90036431	0.00000042
5	1	2017.90025857	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.1873	0.005596	0.000200	6.058E-6	1.913E-7	7.241E-9	2.59E-10
2	0.005596	0.1533	0.005479	0.000166	5.24E-6	1.984E-7	7.085E-9
3	0.000200	0.005479	0.1795	0.005437	0.000172	6.498E-6	2.321E-7
4	6.058E-6	0.000166	0.005437	0.1510	0.004766	0.000180	6.446E-6
5	1.913E-7	5.24E-6	0.000172	0.004766	0.1380	0.005223	0.000187
6	7.241E-9	1.984E-7	6.498E-6	0.000180	0.005223	0.1813	0.006475
7	2.59E-10	7.085E-9	2.321E-7	6.446E-6	0.000187	0.006475	0.2120

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.03303	0.001091	0.000036	1.19E-6	3.93E-8	1.298E-9
2	0.03303	1.0000	0.03303	0.001091	0.000036	1.19E-6	3.93E-8
3	0.001091	0.03303	1.0000	0.03303	0.001091	0.000036	1.19E-6
4	0.000036	0.001091	0.03303	1.0000	0.03303	0.001091	0.000036
5	1.19E-6	0.000036	0.001091	0.03303	1.0000	0.03303	0.001091
6	3.93E-8	1.19E-6	0.000036	0.001091	0.03303	1.0000	0.03303
7	1.298E-9	3.93E-8	1.19E-6	0.000036	0.001091	0.03303	1.0000

Estimated G Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	0.3919

Estimated G Correlation Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	1.0000

Estimated V Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5791	0.3975	0.3921	0.3919	0.3919	0.3919	0.3919
2	0.3975	0.5452	0.3974	0.3921	0.3919	0.3919	0.3919
3	0.3921	0.3974	0.5714	0.3973	0.3921	0.3919	0.3919
4	0.3919	0.3921	0.3973	0.5429	0.3967	0.3921	0.3919
5	0.3919	0.3919	0.3921	0.3967	0.5298	0.3971	0.3921
6	0.3919	0.3919	0.3919	0.3921	0.3971	0.5732	0.3984
7	0.3919	0.3919	0.3919	0.3919	0.3921	0.3984	0.6039

Estimated V Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7074	0.6816	0.6989	0.7074	0.6802	0.6626
2	0.7074	1.0000	0.7120	0.7206	0.7291	0.7010	0.6830
3	0.6816	0.7120	1.0000	0.7134	0.7126	0.6848	0.6671
4	0.6989	0.7206	0.7134	1.0000	0.7396	0.7029	0.6845
5	0.7074	0.7291	0.7126	0.7396	1.0000	0.7206	0.6931
6	0.6802	0.7010	0.6848	0.7029	0.7206	1.0000	0.6771
7	0.6626	0.6830	0.6671	0.6845	0.6931	0.6771	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	0.3919	0.04210	9.31	<.0001
Var(1)	PersonID	0.1873	0.02192	8.54	<.0001
Var(2)	PersonID	0.1533	0.01835	8.35	<.0001
Var(3)	PersonID	0.1795	0.02134	8.41	<.0001
Var(4)	PersonID	0.1510	0.01844	8.19	<.0001
Var(5)	PersonID	0.1380	0.01702	8.10	<.0001
Var(6)	PersonID	0.1813	0.02136	8.49	<.0001
Var(7)	PersonID	0.2120	0.02396	8.85	<.0001
ARH(1)	PersonID	0.03303	0.03705	0.89	0.3727

Fit Statistics
-2 Res Log Likelihood	2017.9
AIC (smaller is better)	2035.9
AICC (smaller is better)	2036.0
BIC (smaller is better)	2065.6

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
8	1055.56	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2017.9	9	2035.9	2036.0	2047.9	2065.6	2074.6

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7374	0.04572	198	81.74	<.0001	0.05	3.6473	3.8276

Likelihood Ratio Test for RIARH1 vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RIARH1	2017.9	9	2035.9	2065.6	.	.	.
UN	1983.1	28	2039.1	2131.5	34.7937	19	0.014787

Likelihood Ratio Test for RIAR1 vs. RIARH1

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RIAR1	2027.4	3	2033.4	2043.3	.	.	.
RIARH1	2017.9	9	2035.9	2065.6	9.52131	6	0.14631

Ch 4: Empty Means, Random Intercept in G

1-Lag Toeplitz R

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structures	Unstructured, Banded Toeplitz
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Profile
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	3
Columns in X	1
Columns in Z Per Subject	1
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2027.75335584	0.00006409
2	1	2027.73745417	0.00000004
3	1	2027.73744444	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.1723	0.006829
2	0.006829	0.1723	0.006829
3		0.006829	0.1723	0.006829
4			0.006829	0.1723	0.006829
5				0.006829	0.1723	0.006829
6					0.006829	0.1723	0.006829
7						0.006829	0.1723

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.03962
2	0.03962	1.0000	0.03962
3		0.03962	1.0000	0.03962
4			0.03962	1.0000	0.03962
5				0.03962	1.0000	0.03962
6					0.03962	1.0000	0.03962
7						0.03962	1.0000

Estimated G Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	0.3881

Estimated G Correlation Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	1.0000

Estimated V Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5604	0.3949	0.3881	0.3881	0.3881	0.3881	0.3881
2	0.3949	0.5604	0.3949	0.3881	0.3881	0.3881	0.3881
3	0.3881	0.3949	0.5604	0.3949	0.3881	0.3881	0.3881
4	0.3881	0.3881	0.3949	0.5604	0.3949	0.3881	0.3881
5	0.3881	0.3881	0.3881	0.3949	0.5604	0.3949	0.3881
6	0.3881	0.3881	0.3881	0.3881	0.3949	0.5604	0.3949
7	0.3881	0.3881	0.3881	0.3881	0.3881	0.3949	0.5604

Estimated V Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7047	0.6925	0.6925	0.6925	0.6925	0.6925
2	0.7047	1.0000	0.7047	0.6925	0.6925	0.6925	0.6925
3	0.6925	0.7047	1.0000	0.7047	0.6925	0.6925	0.6925
4	0.6925	0.6925	0.7047	1.0000	0.7047	0.6925	0.6925
5	0.6925	0.6925	0.6925	0.7047	1.0000	0.7047	0.6925
6	0.6925	0.6925	0.6925	0.6925	0.7047	1.0000	0.7047
7	0.6925	0.6925	0.6925	0.6925	0.6925	0.7047	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	0.3881	0.04175	9.30	<.0001
TOEP(2)	PersonID	0.006829	0.005664	1.21	0.2279
Residual		0.1723	0.007383	23.35	<.0001

Fit Statistics
-2 Res Log Likelihood	2027.7
AIC (smaller is better)	2033.7
AICC (smaller is better)	2033.8
BIC (smaller is better)	2043.6

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
2	1045.72	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2027.7	3	2033.7	2033.8	2037.7	2043.6	2046.6

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7356	0.04556	198	82.00	<.0001	0.05	3.6457	3.8254

Likelihood Ratio Test for RITOEP2 vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEP2	2027.7	3	2033.7	2043.6	.	.	.
UN	1983.1	28	2039.1	2131.5	44.6309	25	.009209891

Likelihood Ratio Test for RIDIAG vs. RITOEP2

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RIDIAG	2029.2	2	2033.2	2039.8	.	.	.
RITOEP2	2027.7	3	2033.7	2043.6	1.46383	1	0.22632

Ch 4: Empty Means, Random Intercept in G

1-Lag Toeplitz Heterogeneous R

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structures	Unstructured, Heterogeneous Toeplitz
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	9
Columns in X	1
Columns in Z Per Subject	1
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2029.35779650	0.03428225
2	1	2019.45084199	0.00496126
3	1	2018.08001565	0.00019383
4	1	2018.03039279	0.00000037
5	1	2018.03029991	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.1875	0.004630
2	0.004630	0.1532	0.004522
3		0.004522	0.1788	0.004480
4			0.004480	0.1504	0.003928
5				0.003928	0.1374	0.004307
6					0.004307	0.1808	0.005348
7						0.005348	0.2119

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.02732
2	0.02732	1.0000	0.02732
3		0.02732	1.0000	0.02732
4			0.02732	1.0000	0.02732
5				0.02732	1.0000	0.02732
6					0.02732	1.0000	0.02732
7						0.02732	1.0000

Estimated G Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	0.3922

Estimated G Correlation Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	1.0000

Estimated V Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5797	0.3969	0.3922	0.3922	0.3922	0.3922	0.3922
2	0.3969	0.5454	0.3968	0.3922	0.3922	0.3922	0.3922
3	0.3922	0.3968	0.5711	0.3967	0.3922	0.3922	0.3922
4	0.3922	0.3922	0.3967	0.5426	0.3962	0.3922	0.3922
5	0.3922	0.3922	0.3922	0.3962	0.5297	0.3965	0.3922
6	0.3922	0.3922	0.3922	0.3922	0.3965	0.5730	0.3976
7	0.3922	0.3922	0.3922	0.3922	0.3922	0.3976	0.6041

Estimated V Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7058	0.6817	0.6994	0.7078	0.6806	0.6628
2	0.7058	1.0000	0.7109	0.7210	0.7297	0.7016	0.6833
3	0.6817	0.7109	1.0000	0.7127	0.7132	0.6857	0.6678
4	0.6994	0.7210	0.7127	1.0000	0.7390	0.7034	0.6851
5	0.7078	0.7297	0.7132	0.7390	1.0000	0.7198	0.6934
6	0.6806	0.7016	0.6857	0.7034	0.7198	1.0000	0.6757
7	0.6628	0.6833	0.6678	0.6851	0.6934	0.6757	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	0.3922	0.04209	9.32	<.0001
Var(1)	PersonID	0.1875	0.02194	8.55	<.0001
Var(2)	PersonID	0.1532	0.01833	8.36	<.0001
Var(3)	PersonID	0.1788	0.02116	8.45	<.0001
Var(4)	PersonID	0.1504	0.01827	8.23	<.0001
Var(5)	PersonID	0.1374	0.01688	8.14	<.0001
Var(6)	PersonID	0.1808	0.02124	8.51	<.0001
Var(7)	PersonID	0.2119	0.02393	8.86	<.0001
TOEPH(1)	PersonID	0.02732	0.03298	0.83	0.4074

Fit Statistics
-2 Res Log Likelihood	2018.0
AIC (smaller is better)	2036.0
AICC (smaller is better)	2036.2
BIC (smaller is better)	2065.7

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
8	1055.43	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2018.0	9	2036.0	2036.2	2048.0	2065.7	2074.7

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7374	0.04572	198	81.74	<.0001	0.05	3.6472	3.8276

Likelihood Ratio Test for RITOEPH2 vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEPH2	2018.0	9	2036.0	2065.7	.	.	.
UN	1983.1	28	2039.1	2131.5	34.9237	19	0.014265

Likelihood Ratio Test for RITOEP2 vs. RITOEPH2

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEP2	2027.7	3	2033.7	2043.6	.	.	.
RITOEPH2	2018.0	9	2036.0	2065.7	9.70714	6	0.13754

Likelihood Ratio Test for RIDIAGH vs. RITOEPH2

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RIDIAGH	2018.7	8	2034.7	2061.1	.	.	.
RITOEPH2	2018.0	9	2036.0	2065.7	0.67692	1	0.41065

Ch 4: Empty Means, Random Intercept in G

2-Lag Toeplitz R

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structures	Unstructured, Banded Toeplitz
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Profile
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	4
Columns in X	1
Columns in Z Per Subject	1
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2016.79238957	0.00006248
2	1	2016.77653728	0.00000004
3	1	2016.77652742	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.1805	0.01653	0.02290
2	0.01653	0.1805	0.01653	0.02290
3	0.02290	0.01653	0.1805	0.01653	0.02290
4		0.02290	0.01653	0.1805	0.01653	0.02290
5			0.02290	0.01653	0.1805	0.01653	0.02290
6				0.02290	0.01653	0.1805	0.01653
7					0.02290	0.01653	0.1805

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.09156	0.1268
2	0.09156	1.0000	0.09156	0.1268
3	0.1268	0.09156	1.0000	0.09156	0.1268
4		0.1268	0.09156	1.0000	0.09156	0.1268
5			0.1268	0.09156	1.0000	0.09156	0.1268
6				0.1268	0.09156	1.0000	0.09156
7					0.1268	0.09156	1.0000

Estimated G Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	0.3797

Estimated G Correlation Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	1.0000

Estimated V Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5602	0.3962	0.4026	0.3797	0.3797	0.3797	0.3797
2	0.3962	0.5602	0.3962	0.4026	0.3797	0.3797	0.3797
3	0.4026	0.3962	0.5602	0.3962	0.4026	0.3797	0.3797
4	0.3797	0.4026	0.3962	0.5602	0.3962	0.4026	0.3797
5	0.3797	0.3797	0.4026	0.3962	0.5602	0.3962	0.4026
6	0.3797	0.3797	0.3797	0.4026	0.3962	0.5602	0.3962
7	0.3797	0.3797	0.3797	0.3797	0.4026	0.3962	0.5602

Estimated V Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7072	0.7186	0.6777	0.6777	0.6777	0.6777
2	0.7072	1.0000	0.7072	0.7186	0.6777	0.6777	0.6777
3	0.7186	0.7072	1.0000	0.7072	0.7186	0.6777	0.6777
4	0.6777	0.7186	0.7072	1.0000	0.7072	0.7186	0.6777
5	0.6777	0.6777	0.7186	0.7072	1.0000	0.7072	0.7186
6	0.6777	0.6777	0.6777	0.7186	0.7072	1.0000	0.7072
7	0.6777	0.6777	0.6777	0.6777	0.7186	0.7072	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	0.3797	0.04180	9.08	<.0001
TOEP(2)	PersonID	0.01653	0.007402	2.23	0.0255
TOEP(3)	PersonID	0.02290	0.006934	3.30	0.0010
Residual		0.1805	0.008527	21.17	<.0001

Fit Statistics
-2 Res Log Likelihood	2016.8
AIC (smaller is better)	2024.8
AICC (smaller is better)	2024.8
BIC (smaller is better)	2038.0

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
3	1056.68	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2016.8	4	2024.8	2024.8	2030.1	2038.0	2042.0

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7360	0.04553	198	82.05	<.0001	0.05	3.6463	3.8258

Likelihood Ratio Test for RITOEP3 vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEP3	2016.8	4	2024.8	2038.0	.	.	.
UN	1983.1	28	2039.1	2131.5	33.6699	24	0.090708

Likelihood Ratio Test for RITOEP2 vs. RITOEP3

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEP2	2027.7	3	2033.7	2043.6	.	.	.
RITOEP3	2016.8	4	2024.8	2038.0	10.9609	1	.000930538

Ch 4: Empty Means, Random Intercept in G

2-Lag Toeplitz Heterogeneous R

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structures	Unstructured, Heterogeneous Toeplitz
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	10
Columns in X	1
Columns in Z Per Subject	1
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2019.60539616	0.03200372
2	1	2010.21657427	0.00431967
3	1	2009.00823575	0.00014659
4	1	2008.97016248	0.00000021
5	1	2008.97010899	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.1884	0.01381	0.02283
2	0.01381	0.1569	0.01403	0.01902
3	0.02283	0.01403	0.1947	0.01427	0.02033
4		0.01902	0.01427	0.1622	0.01250	0.02059
5			0.02033	0.01250	0.1494	0.01331	0.02157
6				0.02059	0.01331	0.1840	0.01612
7					0.02157	0.01612	0.2190

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.08029	0.1192
2	0.08029	1.0000	0.08029	0.1192
3	0.1192	0.08029	1.0000	0.08029	0.1192
4		0.1192	0.08029	1.0000	0.08029	0.1192
5			0.1192	0.08029	1.0000	0.08029	0.1192
6				0.1192	0.08029	1.0000	0.08029
7					0.1192	0.08029	1.0000

Estimated G Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	0.3837

Estimated G Correlation Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	1.0000

Estimated V Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5721	0.3975	0.4065	0.3837	0.3837	0.3837	0.3837
2	0.3975	0.5407	0.3977	0.4027	0.3837	0.3837	0.3837
3	0.4065	0.3977	0.5784	0.3980	0.4040	0.3837	0.3837
4	0.3837	0.4027	0.3980	0.5459	0.3962	0.4043	0.3837
5	0.3837	0.3837	0.4040	0.3962	0.5331	0.3970	0.4053
6	0.3837	0.3837	0.3837	0.4043	0.3970	0.5677	0.3998
7	0.3837	0.3837	0.3837	0.3837	0.4053	0.3998	0.6027

Estimated V Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7148	0.7067	0.6866	0.6948	0.6733	0.6535
2	0.7148	1.0000	0.7113	0.7413	0.7147	0.6926	0.6722
3	0.7067	0.7113	1.0000	0.7083	0.7276	0.6696	0.6499
4	0.6866	0.7413	0.7083	1.0000	0.7344	0.7263	0.6690
5	0.6948	0.7147	0.7276	0.7344	1.0000	0.7217	0.7150
6	0.6733	0.6926	0.6696	0.7263	0.7217	1.0000	0.6836
7	0.6535	0.6722	0.6499	0.6690	0.7150	0.6836	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	0.3837	0.04213	9.11	<.0001
Var(1)	PersonID	0.1884	0.02229	8.45	<.0001
Var(2)	PersonID	0.1569	0.01906	8.23	<.0001
Var(3)	PersonID	0.1947	0.02330	8.35	<.0001
Var(4)	PersonID	0.1622	0.01966	8.25	<.0001
Var(5)	PersonID	0.1494	0.01853	8.06	<.0001
Var(6)	PersonID	0.1840	0.02174	8.46	<.0001
Var(7)	PersonID	0.2190	0.02514	8.71	<.0001
TOEPH(1)	PersonID	0.08029	0.03960	2.03	0.0426
TOEPH(2)	PersonID	0.1192	0.03724	3.20	0.0014

Fit Statistics
-2 Res Log Likelihood	2009.0
AIC (smaller is better)	2029.0
AICC (smaller is better)	2029.1
BIC (smaller is better)	2062.0

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
9	1064.49	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2009.0	10	2029.0	2029.1	2042.3	2062.0	2072.0

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7383	0.04568	198	81.83	<.0001	0.05	3.6482	3.8284

Likelihood Ratio Test for RITOEPH3 vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEPH3	2009.0	10	2029.0	2062.0	.	.	.
UN	1983.1	28	2039.1	2131.5	25.8635	18	0.10292

Likelihood Ratio Test for RITOEP3 vs. RITOEPH3

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEP3	2016.8	4	2024.8	2038.0	.	.	.
RITOEPH3	2009.0	10	2029.0	2062.0	7.80642	6	0.25263

Likelihood Ratio Test for RITOEPH2 vs. RITOEPH3

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEPH2	2018.0	9	2036.0	2065.7	.	.	.
RITOEPH3	2009.0	10	2029.0	2062.0	9.06019	1	.002612347

Ch 4: Empty Means, Random Intercept in G

3-Lag Toeplitz R

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structures	Unstructured, Banded Toeplitz
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Profile
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	5
Columns in X	1
Columns in Z Per Subject	1
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2015.84418848	0.00010390
2	1	2015.81781136	0.00000006
3	1	2015.81779532	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.1843	0.02082	0.02707	0.008373
2	0.02082	0.1843	0.02082	0.02707	0.008373
3	0.02707	0.02082	0.1843	0.02082	0.02707	0.008373
4	0.008373	0.02707	0.02082	0.1843	0.02082	0.02707	0.008373
5		0.008373	0.02707	0.02082	0.1843	0.02082	0.02707
6			0.008373	0.02707	0.02082	0.1843	0.02082
7				0.008373	0.02707	0.02082	0.1843

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.1129	0.1469	0.04542
2	0.1129	1.0000	0.1129	0.1469	0.04542
3	0.1469	0.1129	1.0000	0.1129	0.1469	0.04542
4	0.04542	0.1469	0.1129	1.0000	0.1129	0.1469	0.04542
5		0.04542	0.1469	0.1129	1.0000	0.1129	0.1469
6			0.04542	0.1469	0.1129	1.0000	0.1129
7				0.04542	0.1469	0.1129	1.0000

Estimated G Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	0.3756

Estimated G Correlation Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	1.0000

Estimated V Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5600	0.3965	0.4027	0.3840	0.3756	0.3756	0.3756
2	0.3965	0.5600	0.3965	0.4027	0.3840	0.3756	0.3756
3	0.4027	0.3965	0.5600	0.3965	0.4027	0.3840	0.3756
4	0.3840	0.4027	0.3965	0.5600	0.3965	0.4027	0.3840
5	0.3756	0.3840	0.4027	0.3965	0.5600	0.3965	0.4027
6	0.3756	0.3756	0.3840	0.4027	0.3965	0.5600	0.3965
7	0.3756	0.3756	0.3756	0.3840	0.4027	0.3965	0.5600

Estimated V Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7080	0.7191	0.6858	0.6708	0.6708	0.6708
2	0.7080	1.0000	0.7080	0.7191	0.6858	0.6708	0.6708
3	0.7191	0.7080	1.0000	0.7080	0.7191	0.6858	0.6708
4	0.6858	0.7191	0.7080	1.0000	0.7080	0.7191	0.6858
5	0.6708	0.6858	0.7191	0.7080	1.0000	0.7080	0.7191
6	0.6708	0.6708	0.6858	0.7191	0.7080	1.0000	0.7080
7	0.6708	0.6708	0.6708	0.6858	0.7191	0.7080	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	0.3756	0.04198	8.95	<.0001
TOEP(2)	PersonID	0.02082	0.008833	2.36	0.0184
TOEP(3)	PersonID	0.02707	0.008192	3.30	0.0010
TOEP(4)	PersonID	0.008373	0.008568	0.98	0.3284
Residual		0.1843	0.009680	19.04	<.0001

Fit Statistics
-2 Res Log Likelihood	2015.8
AIC (smaller is better)	2025.8
AICC (smaller is better)	2025.9
BIC (smaller is better)	2042.3

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
4	1057.64	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2015.8	5	2025.8	2025.9	2032.5	2042.3	2047.3

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7363	0.04551	198	82.09	<.0001	0.05	3.6466	3.8261

Likelihood Ratio Test for RITOEP4 vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEP4	2015.8	5	2025.8	2042.3	.	.	.
UN	1983.1	28	2039.1	2131.5	32.7112	23	0.086233

Likelihood Ratio Test for RITOEP3 vs. RITOEP4

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEP3	2016.8	4	2024.8	2038.0	.	.	.
RITOEP4	2015.8	5	2025.8	2042.3	0.95873	1	0.32751

Ch 4: Empty Means, Random Intercept in G

3-Lag Toeplitz Heterogeneous R

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structures	Unstructured, Heterogeneous Toeplitz
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	11
Columns in X	1
Columns in Z Per Subject	1
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2016.03334279	0.02429089
2	1	2009.02772099	0.00231233
3	1	2008.39429584	0.00004289
4	1	2008.38326050	0.00000002
5	1	2008.38325573	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.1897	0.01742	0.02688	0.006598
2	0.01742	0.1585	0.01789	0.02253	0.005755
3	0.02688	0.01789	0.2000	0.01843	0.02416	0.007138
4	0.006598	0.02253	0.01843	0.1682	0.01613	0.02445	0.007138
5		0.005755	0.02416	0.01613	0.1532	0.01699	0.02544
6			0.007138	0.02445	0.01699	0.1866	0.02045
7				0.007138	0.02544	0.02045	0.2219

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.1005	0.1380	0.03694
2	0.1005	1.0000	0.1005	0.1380	0.03694
3	0.1380	0.1005	1.0000	0.1005	0.1380	0.03694
4	0.03694	0.1380	0.1005	1.0000	0.1005	0.1380	0.03694
5		0.03694	0.1380	0.1005	1.0000	0.1005	0.1380
6			0.03694	0.1380	0.1005	1.0000	0.1005
7				0.03694	0.1380	0.1005	1.0000

Estimated G Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	0.3801

Estimated G Correlation Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	1.0000

Estimated V Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5698	0.3975	0.4070	0.3867	0.3801	0.3801	0.3801
2	0.3975	0.5385	0.3980	0.4026	0.3859	0.3801	0.3801
3	0.4070	0.3980	0.5801	0.3985	0.4043	0.3872	0.3801
4	0.3867	0.4026	0.3985	0.5483	0.3962	0.4045	0.3872
5	0.3801	0.3859	0.4043	0.3962	0.5332	0.3971	0.4055
6	0.3801	0.3801	0.3872	0.4045	0.3971	0.5667	0.4005
7	0.3801	0.3801	0.3801	0.3872	0.4055	0.4005	0.6020

Estimated V Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7176	0.7079	0.6918	0.6896	0.6689	0.6490
2	0.7176	1.0000	0.7120	0.7409	0.7200	0.6880	0.6675
3	0.7079	0.7120	1.0000	0.7066	0.7268	0.6753	0.6432
4	0.6918	0.7409	0.7066	1.0000	0.7328	0.7257	0.6740
5	0.6896	0.7200	0.7268	0.7328	1.0000	0.7223	0.7158
6	0.6689	0.6880	0.6753	0.7257	0.7223	1.0000	0.6857
7	0.6490	0.6675	0.6432	0.6740	0.7158	0.6857	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	0.3801	0.04236	8.97	<.0001
Var(1)	PersonID	0.1897	0.02260	8.39	<.0001
Var(2)	PersonID	0.1585	0.01940	8.17	<.0001
Var(3)	PersonID	0.2000	0.02495	8.02	<.0001
Var(4)	PersonID	0.1682	0.02166	7.77	<.0001
Var(5)	PersonID	0.1532	0.01960	7.82	<.0001
Var(6)	PersonID	0.1866	0.02239	8.34	<.0001
Var(7)	PersonID	0.2219	0.02592	8.56	<.0001
TOEPH(1)	PersonID	0.1005	0.04714	2.13	0.0330
TOEPH(2)	PersonID	0.1380	0.04346	3.18	0.0015
TOEPH(3)	PersonID	0.03694	0.04735	0.78	0.4353

Fit Statistics
-2 Res Log Likelihood	2008.4
AIC (smaller is better)	2030.4
AICC (smaller is better)	2030.6
BIC (smaller is better)	2066.7

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
10	1065.07	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2008.4	11	2030.4	2030.6	2045.1	2066.7	2077.7

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7388	0.04566	198	81.88	<.0001	0.05	3.6487	3.8288

Likelihood Ratio Test for RITOEPH4 vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEPH4	2008.4	11	2030.4	2066.7	.	.	.
UN	1983.1	28	2039.1	2131.5	25.2767	17	0.088686

Likelihood Ratio Test for RITOEP4 vs. RITOEPH4

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEP4	2015.8	5	2025.8	2042.3	.	.	.
RITOEPH4	2008.4	11	2030.4	2066.7	7.43454	6	0.28252

Likelihood Ratio Test for RITOEPH3 vs. RITOEPH4

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEPH3	2009.0	10	2029.0	2062.0	.	.	.
RITOEPH4	2008.4	11	2030.4	2066.7	0.58685	1	0.44364

Ch 4: Empty Means, Random Intercept in G

4-Lag Toeplitz R

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structures	Unstructured, Banded Toeplitz
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Profile
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	6
Columns in X	1
Columns in Z Per Subject	1
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2012.19631673	0.00011864
2	1	2012.16596815	0.00000008
3	1	2012.16594755	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.1958	0.03242	0.04084	0.01936	0.01900
2	0.03242	0.1958	0.03242	0.04084	0.01936	0.01900
3	0.04084	0.03242	0.1958	0.03242	0.04084	0.01936	0.01900
4	0.01936	0.04084	0.03242	0.1958	0.03242	0.04084	0.01936
5	0.01900	0.01936	0.04084	0.03242	0.1958	0.03242	0.04084
6		0.01900	0.01936	0.04084	0.03242	0.1958	0.03242
7			0.01900	0.01936	0.04084	0.03242	0.1958

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.1656	0.2085	0.09887	0.09703
2	0.1656	1.0000	0.1656	0.2085	0.09887	0.09703
3	0.2085	0.1656	1.0000	0.1656	0.2085	0.09887	0.09703
4	0.09887	0.2085	0.1656	1.0000	0.1656	0.2085	0.09887
5	0.09703	0.09887	0.2085	0.1656	1.0000	0.1656	0.2085
6		0.09703	0.09887	0.2085	0.1656	1.0000	0.1656
7			0.09703	0.09887	0.2085	0.1656	1.0000

Estimated G Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	0.3645

Estimated G Correlation Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	1.0000

Estimated V Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5603	0.3969	0.4054	0.3839	0.3835	0.3645	0.3645
2	0.3969	0.5603	0.3969	0.4054	0.3839	0.3835	0.3645
3	0.4054	0.3969	0.5603	0.3969	0.4054	0.3839	0.3835
4	0.3839	0.4054	0.3969	0.5603	0.3969	0.4054	0.3839
5	0.3835	0.3839	0.4054	0.3969	0.5603	0.3969	0.4054
6	0.3645	0.3835	0.3839	0.4054	0.3969	0.5603	0.3969
7	0.3645	0.3645	0.3835	0.3839	0.4054	0.3969	0.5603

Estimated V Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7084	0.7234	0.6851	0.6844	0.6505	0.6505
2	0.7084	1.0000	0.7084	0.7234	0.6851	0.6844	0.6505
3	0.7234	0.7084	1.0000	0.7084	0.7234	0.6851	0.6844
4	0.6851	0.7234	0.7084	1.0000	0.7084	0.7234	0.6851
5	0.6844	0.6851	0.7234	0.7084	1.0000	0.7084	0.7234
6	0.6505	0.6844	0.6851	0.7234	0.7084	1.0000	0.7084
7	0.6505	0.6505	0.6844	0.6851	0.7234	0.7084	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	0.3645	0.04243	8.59	<.0001
TOEP(2)	PersonID	0.03242	0.01145	2.83	0.0046
TOEP(3)	PersonID	0.04084	0.01159	3.52	0.0004
TOEP(4)	PersonID	0.01936	0.01053	1.84	0.0659
TOEP(5)	PersonID	0.01900	0.01004	1.89	0.0585
Residual		0.1958	0.01231	15.90	<.0001

Fit Statistics
-2 Res Log Likelihood	2012.2
AIC (smaller is better)	2024.2
AICC (smaller is better)	2024.2
BIC (smaller is better)	2044.0

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
5	1061.29	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2012.2	6	2024.2	2024.2	2032.2	2044.0	2050.0

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7362	0.04551	198	82.10	<.0001	0.05	3.6465	3.8259

Likelihood Ratio Test for RITOEP5 vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEP5	2012.2	6	2024.2	2044.0	.	.	.
UN	1983.1	28	2039.1	2131.5	29.0594	22	0.14317

Likelihood Ratio Test for RITOEP4 vs. RITOEP5

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEP4	2015.8	5	2025.8	2042.3	.	.	.
RITOEP5	2012.2	6	2024.2	2044.0	3.65185	1	0.056007

Ch 4: Empty Means, Random Intercept in G

4-Lag Toeplitz Heterogeneous R

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structures	Unstructured, Heterogeneous Toeplitz
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	12
Columns in X	1
Columns in Z Per Subject	1
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2014.37158551	0.02484888
2	1	2007.14087828	0.00273782
3	1	2006.38018297	0.00006792
4	1	2006.36256340	0.00000005
5	1	2006.36255020	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.1957	0.02671	0.03888	0.01562	0.01398
2	0.02671	0.1670	0.02783	0.03302	0.01387	0.01404
3	0.03888	0.02783	0.2126	0.02888	0.03581	0.01702	0.01702
4	0.01562	0.03302	0.02888	0.1798	0.02552	0.03581	0.01681
5	0.01398	0.01387	0.03581	0.02552	0.1660	0.02668	0.03696
6		0.01404	0.01702	0.03581	0.02668	0.1964	0.03116
7			0.01702	0.01681	0.03696	0.03116	0.2265

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.1477	0.1906	0.08329	0.07755
2	0.1477	1.0000	0.1477	0.1906	0.08329	0.07755
3	0.1906	0.1477	1.0000	0.1477	0.1906	0.08329	0.07755
4	0.08329	0.1906	0.1477	1.0000	0.1477	0.1906	0.08329
5	0.07755	0.08329	0.1906	0.1477	1.0000	0.1477	0.1906
6		0.07755	0.08329	0.1906	0.1477	1.0000	0.1477
7			0.07755	0.08329	0.1906	0.1477	1.0000

Estimated G Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	0.3706

Estimated G Correlation Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	1.0000

Estimated V Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5664	0.3973	0.4095	0.3863	0.3846	0.3706	0.3706
2	0.3973	0.5376	0.3985	0.4036	0.3845	0.3847	0.3706
3	0.4095	0.3985	0.5832	0.3995	0.4064	0.3877	0.3877
4	0.3863	0.4036	0.3995	0.5504	0.3962	0.4064	0.3874
5	0.3846	0.3845	0.4064	0.3962	0.5367	0.3973	0.4076
6	0.3706	0.3847	0.3877	0.4064	0.3973	0.5671	0.4018
7	0.3706	0.3706	0.3877	0.3874	0.4076	0.4018	0.5972

Estimated V Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7201	0.7125	0.6918	0.6976	0.6540	0.6373
2	0.7201	1.0000	0.7116	0.7421	0.7158	0.6967	0.6541
3	0.7125	0.7116	1.0000	0.7051	0.7265	0.6741	0.6569
4	0.6918	0.7421	0.7051	1.0000	0.7289	0.7275	0.6758
5	0.6976	0.7158	0.7265	0.7289	1.0000	0.7202	0.7200
6	0.6540	0.6967	0.6741	0.7275	0.7202	1.0000	0.6905
7	0.6373	0.6541	0.6569	0.6758	0.7200	0.6905	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	0.3706	0.04290	8.64	<.0001
Var(1)	PersonID	0.1957	0.02393	8.18	<.0001
Var(2)	PersonID	0.1670	0.02146	7.78	<.0001
Var(3)	PersonID	0.2126	0.02757	7.71	<.0001
Var(4)	PersonID	0.1798	0.02454	7.32	<.0001
Var(5)	PersonID	0.1660	0.02297	7.23	<.0001
Var(6)	PersonID	0.1964	0.02471	7.95	<.0001
Var(7)	PersonID	0.2265	0.02681	8.45	<.0001
TOEPH(1)	PersonID	0.1477	0.05586	2.64	0.0082
TOEPH(2)	PersonID	0.1906	0.05495	3.47	0.0005
TOEPH(3)	PersonID	0.08329	0.05423	1.54	0.1246
TOEPH(4)	PersonID	0.07755	0.05179	1.50	0.1342

Fit Statistics
-2 Res Log Likelihood	2006.4
AIC (smaller is better)	2030.4
AICC (smaller is better)	2030.6
BIC (smaller is better)	2069.9

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
11	1067.09	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2006.4	12	2030.4	2030.6	2046.4	2069.9	2081.9

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7389	0.04564	198	81.91	<.0001	0.05	3.6488	3.8289

Likelihood Ratio Test for RITOEPH5 vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEPH5	2006.4	12	2030.4	2069.9	.	.	.
UN	1983.1	28	2039.1	2131.5	23.2560	16	0.10706

Likelihood Ratio Test for RITOEP5 vs. RITOEPH5

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEP5	2012.2	6	2024.2	2044.0	.	.	.
RITOEPH5	2006.4	12	2030.4	2069.9	5.80340	6	0.44557

Likelihood Ratio Test for RITOEPH4 vs. RITOEPH5

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEPH4	2008.4	11	2030.4	2066.7	.	.	.
RITOEPH5	2006.4	12	2030.4	2069.9	2.02071	1	0.15517

Ch 4: Empty Means, Random Intercept in G

5-Lag Toeplitz R

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structures	Unstructured, Banded Toeplitz
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Profile
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	7
Columns in X	1
Columns in Z Per Subject	1
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	2	2010.00985165	0.00039380
2	1	2009.90646393	0.00000142
3	1	2009.90610463	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.2132	0.05086	0.05855	0.03737	0.03460	0.02321
2	0.05086	0.2132	0.05086	0.05855	0.03737	0.03460	0.02321
3	0.05855	0.05086	0.2132	0.05086	0.05855	0.03737	0.03460
4	0.03737	0.05855	0.05086	0.2132	0.05086	0.05855	0.03737
5	0.03460	0.03737	0.05855	0.05086	0.2132	0.05086	0.05855
6	0.02321	0.03460	0.03737	0.05855	0.05086	0.2132	0.05086
7		0.02321	0.03460	0.03737	0.05855	0.05086	0.2132

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.2386	0.2746	0.1753	0.1623	0.1088
2	0.2386	1.0000	0.2386	0.2746	0.1753	0.1623	0.1088
3	0.2746	0.2386	1.0000	0.2386	0.2746	0.1753	0.1623
4	0.1753	0.2746	0.2386	1.0000	0.2386	0.2746	0.1753
5	0.1623	0.1753	0.2746	0.2386	1.0000	0.2386	0.2746
6	0.1088	0.1623	0.1753	0.2746	0.2386	1.0000	0.2386
7		0.1088	0.1623	0.1753	0.2746	0.2386	1.0000

Estimated G Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	0.3477

Estimated G Correlation Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	1.0000

Estimated V Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5609	0.3986	0.4063	0.3851	0.3823	0.3709	0.3477
2	0.3986	0.5609	0.3986	0.4063	0.3851	0.3823	0.3709
3	0.4063	0.3986	0.5609	0.3986	0.4063	0.3851	0.3823
4	0.3851	0.4063	0.3986	0.5609	0.3986	0.4063	0.3851
5	0.3823	0.3851	0.4063	0.3986	0.5609	0.3986	0.4063
6	0.3709	0.3823	0.3851	0.4063	0.3986	0.5609	0.3986
7	0.3477	0.3709	0.3823	0.3851	0.4063	0.3986	0.5609

Estimated V Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7106	0.7243	0.6865	0.6816	0.6613	0.6199
2	0.7106	1.0000	0.7106	0.7243	0.6865	0.6816	0.6613
3	0.7243	0.7106	1.0000	0.7106	0.7243	0.6865	0.6816
4	0.6865	0.7243	0.7106	1.0000	0.7106	0.7243	0.6865
5	0.6816	0.6865	0.7243	0.7106	1.0000	0.7106	0.7243
6	0.6613	0.6816	0.6865	0.7243	0.7106	1.0000	0.7106
7	0.6199	0.6613	0.6816	0.6865	0.7243	0.7106	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	0.3477	0.04398	7.91	<.0001
TOEP(2)	PersonID	0.05086	0.01732	2.94	0.0033
TOEP(3)	PersonID	0.05855	0.01708	3.43	0.0006
TOEP(4)	PersonID	0.03737	0.01621	2.30	0.0212
TOEP(5)	PersonID	0.03460	0.01463	2.37	0.0180
TOEP(6)	PersonID	0.02321	0.01545	1.50	0.1332
Residual		0.2132	0.01786	11.94	<.0001

Fit Statistics
-2 Res Log Likelihood	2009.9
AIC (smaller is better)	2023.9
AICC (smaller is better)	2024.0
BIC (smaller is better)	2047.0

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
6	1063.55	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2009.9	7	2023.9	2024.0	2033.2	2047.0	2054.0

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7357	0.04552	198	82.07	<.0001	0.05	3.6460	3.8255

Likelihood Ratio Test for RITOEP6 vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEP6	2009.9	7	2023.9	2047.0	.	.	.
UN	1983.1	28	2039.1	2131.5	26.7995	21	0.17759

Likelihood Ratio Test for RITOEP5 vs. RITOEP6

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEP5	2012.2	6	2024.2	2044.0	.	.	.
RITOEP6	2009.9	7	2023.9	2047.0	2.25984	1	0.13277

Ch 4: Empty Means, Random Intercept in G

5-Lag Toeplitz Heterogeneous R

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER4
Dependent Variable	posmood
Covariance Structures	Unstructured, Heterogeneous Toeplitz
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	13
Columns in X	1
Columns in Z Per Subject	1
Subjects	200
Max Obs Per Subject	7

Number of Observations
Number of Observations Read	1370
Number of Observations Used	1370
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	3073.45623703
1	4	2007.19260885	0.00770185
2	1	2005.14691749	0.00033705
3	1	2005.05857849	0.00000068
4	1	2005.05840440	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.2082	0.04154	0.05498	0.03079	0.02673	0.01920
2	0.04154	0.1814	0.04361	0.04754	0.02756	0.02701	0.01905
3	0.05498	0.04361	0.2294	0.04542	0.05127	0.03354	0.03227
4	0.03079	0.04754	0.04542	0.1968	0.04035	0.05140	0.03302
5	0.02673	0.02756	0.05127	0.04035	0.1810	0.04188	0.05238
6	0.01920	0.02701	0.03354	0.05140	0.04188	0.2121	0.04817
7		0.01905	0.03227	0.03302	0.05238	0.04817	0.2395

Estimated R Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.2138	0.2516	0.1521	0.1377	0.09139
2	0.2138	1.0000	0.2138	0.2516	0.1521	0.1377	0.09139
3	0.2516	0.2138	1.0000	0.2138	0.2516	0.1521	0.1377
4	0.1521	0.2516	0.2138	1.0000	0.2138	0.2516	0.1521
5	0.1377	0.1521	0.2516	0.2138	1.0000	0.2138	0.2516
6	0.09139	0.1377	0.1521	0.2516	0.2138	1.0000	0.2138
7		0.09139	0.1377	0.1521	0.2516	0.2138	1.0000

Estimated G Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	0.3562

Estimated G Correlation Matrix
Row	Effect	PersonID: Person ID variable	Col1
1	Intercept	1	1.0000

Estimated V Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	0.5644	0.3978	0.4112	0.3870	0.3829	0.3754	0.3562
2	0.3978	0.5376	0.3998	0.4038	0.3838	0.3832	0.3753
3	0.4112	0.3998	0.5856	0.4016	0.4075	0.3898	0.3885
4	0.3870	0.4038	0.4016	0.5531	0.3966	0.4076	0.3892
5	0.3829	0.3838	0.4075	0.3966	0.5372	0.3981	0.4086
6	0.3754	0.3832	0.3898	0.4076	0.3981	0.5683	0.4044
7	0.3562	0.3753	0.3885	0.3892	0.4086	0.4044	0.5957

Estimated V Correlation Matrix for PersonID 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7
1	1.0000	0.7221	0.7152	0.6927	0.6954	0.6629	0.6143
2	0.7221	1.0000	0.7126	0.7404	0.7141	0.6933	0.6631
3	0.7152	0.7126	1.0000	0.7057	0.7265	0.6756	0.6577
4	0.6927	0.7404	0.7057	1.0000	0.7275	0.7271	0.6781
5	0.6954	0.7141	0.7265	0.7275	1.0000	0.7205	0.7223
6	0.6629	0.6933	0.6756	0.7271	0.7205	1.0000	0.6950
7	0.6143	0.6631	0.6577	0.6781	0.7223	0.6950	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	0.3562	0.04480	7.95	<.0001
Var(1)	PersonID	0.2082	0.02799	7.44	<.0001
Var(2)	PersonID	0.1814	0.02617	6.93	<.0001
Var(3)	PersonID	0.2294	0.03259	7.04	<.0001
Var(4)	PersonID	0.1968	0.03027	6.50	<.0001
Var(5)	PersonID	0.1810	0.02805	6.45	<.0001
Var(6)	PersonID	0.2121	0.02948	7.19	<.0001
Var(7)	PersonID	0.2395	0.03073	7.79	<.0001
TOEPH(1)	PersonID	0.2138	0.07300	2.93	0.0034
TOEPH(2)	PersonID	0.2516	0.06956	3.62	0.0003
TOEPH(3)	PersonID	0.1521	0.07309	2.08	0.0375
TOEPH(4)	PersonID	0.1377	0.06651	2.07	0.0384
TOEPH(5)	PersonID	0.09139	0.07355	1.24	0.2140

Fit Statistics
-2 Res Log Likelihood	2005.1
AIC (smaller is better)	2031.1
AICC (smaller is better)	2031.3
BIC (smaller is better)	2073.9

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
12	1068.40	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
2005.1	13	2031.1	2031.3	2048.4	2073.9	2086.9

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	3.7390	0.04565	197	81.90	<.0001	0.05	3.6489	3.8290

Likelihood Ratio Test for RITOEPH6 vs. UN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEPH6	2005.1	13	2031.1	2073.9	.	.	.
UN	1983.1	28	2039.1	2131.5	21.9518	15	0.10907

Likelihood Ratio Test for RITOEP6 vs. RITOEPH6

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEP6	2009.9	7	2023.9	2047.0	.	.	.
RITOEPH6	2005.1	13	2031.1	2073.9	4.84770	6	0.56349

Likelihood Ratio Test for RITOEPH5 vs. RITOEPH6

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
RITOEPH5	2006.4	12	2030.4	2069.9	.	.	.
RITOEPH6	2005.1	13	2031.1	2073.9	1.30415	1	0.25346